Chapter 25
Capacitance
Suppose we have a conductor carrying a net chargeCQand a second conductor carrying a net chargeQ;
and suppose the two charges are separated by a fixed distance. Such a device is called acapacitor(or
condenser, an old-fashioned term). The more charge is put on the two conductors of the capacitor, the greater
the potential difference between them. In fact, we find that the potential difference isproportional tothe
amount of charge:QDCV, whereCis called thecapacitance:
CD
Q
V
: (25.1)
Capacitance is measured in units offarads(F), named for English physicist Michael Faraday. One farad is
equal to one coulomb per volt (1 FD1 C/V), and is a very large unit of capacitance. For most laboratory
applications, we will be working with units of microfarads (F), nanofarads (nF), and picofarads (pF).
The reciprocal of capacitance is called theelastanceS:
SD
1
C
: (25.2)
Elastance has units of F^1 , sometimes called adaraf(“farad” spelled backwards).
25.1 Parallel-Plate Capacitor
One common capacitor configuration consists of two parallel plates (each with areaA), separated by a dis-
tanced(Fig. 25.1). As you can see in the figure, the electric field between the plates of the capacitor is nearly
uniform, except near the edges where there are some edge effects.
To find an expression for the capacitance of the parallel-plate capacitor, we apply Gauss’s law to an
imaginary pillbox-shaped Gaussian surface that has one flat end of areaAin the region between the plates,
and the other in the region to the left of the left plate. The electric flux through all faces of the surface except
the face between the plates will be zero; for that face the electric flux will beˆeDEA; then by Gauss’s law,
ˆEDEAD
Q
" 0
: (25.3)
Since the potential difference between the plates isVDEd, we have
VD
Qd
" 0 A